divide vertex into two
In this case beveling vertex won't really help as it will create Ngon with too many sides:



While it's possible to fix that Ngon to desired face later it can be cumbersome as original vertices position won't be the case any more.
Instead you can try Rip tool to detach some faces, fill new one and split it. Then dissolve unnecessary geometry. Note though that both procedures - beveling and merging vs ripping and dissolving - take nearly the same amount of effort. 

Select vertex where edges are connecting (by the way too many edges are joining at one point there). Then press V to execute Rip tool. Your mouse cursor will affect which part is being ripped, in the case below mouse cursor was to the left top so to rip left faces.



Fill a new face there and split it at the vertices in the middle with Connect Vertex Path tool (J); select vertices first and then execute the tool. It will split the face into 2 triangles.

Then merge unncessary vertex and dissolve edges which are no longer needed.



The result isn't clean, it's more of a middle position between further retopology.